Just testbench changes (76fd64f3) · Commits · Elphel / image-compression

SaveableEncoderDecoder.ipynb

+18 −13

Original line number	Original line	Diff line number	Diff line
	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	import numpy as np		import numpy as np
	from matplotlib import pyplot as plt		from matplotlib import pyplot as plt
	from itertools import product		from itertools import product
	import os		import os
	import sys		import sys
	from PIL import Image		from PIL import Image
	from scipy.optimize import minimize,linprog		from scipy.optimize import minimize,linprog
	from sklearn.neighbors import KernelDensity		from sklearn.neighbors import KernelDensity
	from collections import Counter		from collections import Counter
	import numpy.linalg as la		import numpy.linalg as la
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def file_extractor(dirname="images"):		def file_extractor(dirname="images"):
	files = os.listdir(dirname)		files = os.listdir(dirname)
	scenes = []		scenes = []
	for file in files:		for file in files:
	if file == '.DS_Store':		if file == '.DS_Store':
	continue		continue
	else:		else:
	scenes.append(os.path.join(dirname, file))		scenes.append(os.path.join(dirname, file))
	return scenes		return scenes

	def image_extractor(scenes):		def image_extractor(scenes):
	image_folder = []		image_folder = []
	for scene in scenes:		for scene in scenes:
	files = os.listdir(scene)		files = os.listdir(scene)
	for file in files:		for file in files:
	if file[-5:] != ".tiff" or file[-7:] == "_6.tiff":		if file[-5:] != ".tiff" or file[-7:] == "_6.tiff":
	continue		continue
	else:		else:
	image_folder.append(os.path.join(scene, file))		image_folder.append(os.path.join(scene, file))
	return image_folder #returns a list of file paths to .tiff files in the specified directory given in file_extractor		return image_folder #returns a list of file paths to .tiff files in the specified directory given in file_extractor

	def im_distribution(images, num):		def im_distribution(images, num):
	"""		"""
	Function that extracts tiff files from specific cameras and returns a list of all		Function that extracts tiff files from specific cameras and returns a list of all
	the tiff files corresponding to that camera. i.e. all pictures labeled "_7.tiff" or otherwise		the tiff files corresponding to that camera. i.e. all pictures labeled "_7.tiff" or otherwise
	specified camera numbers.		specified camera numbers.

	Parameters:		Parameters:
	images (list): list of all tiff files, regardless of classification. This is NOT a list of directories but		images (list): list of all tiff files, regardless of classification. This is NOT a list of directories but
	of specific tiff files that can be opened right away. This is the list that we iterate through and		of specific tiff files that can be opened right away. This is the list that we iterate through and
	divide.		divide.

	num (str): a string designation for the camera number that we want to extract i.e. "14" for double digits		num (str): a string designation for the camera number that we want to extract i.e. "14" for double digits
	of "_1" for single digits.		of "_1" for single digits.

	Returns:		Returns:
	tiff (list): A list of tiff files that have the specified designation from num. They are the files extracted		tiff (list): A list of tiff files that have the specified designation from num. They are the files extracted
	from the 'images' list that correspond to the given num.		from the 'images' list that correspond to the given num.
	"""		"""
	tiff = []		tiff = []
	for im in images:		for im in images:
	if im[-7:-5] == num:		if im[-7:-5] == num:
	tiff.append(im)		tiff.append(im)
	return tiff		return tiff
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def predict_pix(tiff_image_path, difference = True):		def predict_pix(tiff_image_path, difference = True):
	"""		"""
	This function predict the pixel values excluding the boundary.		This function predict the pixel values excluding the boundary.
	Using the 4 neighbor pixel values and MSE to predict the next pixel value		Using the 4 neighbor pixel values and MSE to predict the next pixel value
	(-1,1) (0,1) (1,1) => relative position of the 4 other given values		(-1,1) (0,1) (1,1) => relative position of the 4 other given values
	(-1,0) (0,0) => (0,0) is the one we want to predict		(-1,0) (0,0) => (0,0) is the one we want to predict
	take the derivative of mean square error to solve for the system of equation		take the derivative of mean square error to solve for the system of equation
	A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])		A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])
	A @ [a, b, c] = [-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3] where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)		A @ [a, b, c] = [-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3] where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)
	and the predicted pixel value is c.		and the predicted pixel value is c.

	Input:		Input:
	tiff_image_path (string): path to the tiff file		tiff_image_path (string): path to the tiff file

	Return:		Return:
	image ndarray(512 X 640): original image		image ndarray(512 X 640): original image
	predict ndarray(325380,): predicted image excluding the boundary		predict ndarray(325380,): predicted image excluding the boundary
	diff. ndarray(325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary		diff. ndarray(325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary
	ELSE: the residuals of the four nearest pixels to a fitted hyperplane		ELSE: the residuals of the four nearest pixels to a fitted hyperplane
	error ndarray(325380,): difference between the original image and predicted image		error ndarray(325380,): difference between the original image and predicted image
	A ndarray(3 X 3): system of equation		A ndarray(3 X 3): system of equation
	"""		"""
	image_obj = Image.open(tiff_image_path) #Open the image and read it as an Image object		image_obj = Image.open(tiff_image_path) #Open the image and read it as an Image object
	image_array = np.array(image_obj)[1:,:].astype(int) #Convert to an array, leaving out the first row because the first row is just housekeeping data		image_array = np.array(image_obj)[1:,:].astype(int) #Convert to an array, leaving out the first row because the first row is just housekeeping data
	# image_array = image_array.astype(int)		# image_array = image_array.astype(int)
	A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation		A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation
	# where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)		# where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)
	z0 = image_array[0:-2,0:-2] # get all the first pixel for the entire image		z0 = image_array[0:-2,0:-2] # get all the first pixel for the entire image
	z1 = image_array[0:-2,1:-1] # get all the second pixel for the entire image		z1 = image_array[0:-2,1:-1] # get all the second pixel for the entire image
	z2 = image_array[0:-2,2::] # get all the third pixel for the entire image		z2 = image_array[0:-2,2::] # get all the third pixel for the entire image
	z3 = image_array[1:-1,0:-2] # get all the forth pixel for the entire image		z3 = image_array[1:-1,0:-2] # get all the forth pixel for the entire image

	# calculate the out put of the system of equation		# calculate the out put of the system of equation
	y0 = np.ravel(-z0+z2-z3)		y0 = np.ravel(-z0+z2-z3)
	y1 = np.ravel(z0+z1+z2)		y1 = np.ravel(z0+z1+z2)
	y2 = np.ravel(-z0-z1-z2-z3)		y2 = np.ravel(-z0-z1-z2-z3)
	y = np.vstack((y0,y1,y2))		y = np.vstack((y0,y1,y2))

	# use numpy solver to solve the system of equations all at once		# use numpy solver to solve the system of equations all at once
	#predict = np.floor(np.linalg.solve(A,y)[-1])		#predict = np.floor(np.linalg.solve(A,y)[-1])
	predict = np.round(np.round((np.linalg.solve(A,y)[-1]),1))		predict = np.round(np.round((np.linalg.solve(A,y)[-1]),1))

	#Matrix system of points that will be used to solve the least squares fitting hyperplane		#Matrix system of points that will be used to solve the least squares fitting hyperplane
	points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])		points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])

	# flatten the neighbor pixlels and stack them together		# flatten the neighbor pixlels and stack them together
	z0 = np.ravel(z0)		z0 = np.ravel(z0)
	z1 = np.ravel(z1)		z1 = np.ravel(z1)
	z2 = np.ravel(z2)		z2 = np.ravel(z2)
	z3 = np.ravel(z3)		z3 = np.ravel(z3)
	neighbor = np.vstack((z0,z1,z2,z3)).T		neighbor = np.vstack((z0,z1,z2,z3)).T

	if difference:		if difference:
	# calculate the difference		# calculate the difference
	diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)		diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)

	else:		else:
	#Compute the best fitting hyperplane using least squares		#Compute the best fitting hyperplane using least squares
	#The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the		#The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the
	#points to the hyperplane), it is a measure of gradient		#points to the hyperplane), it is a measure of gradient
	f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None)		f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None)
	diff = diff.astype(int)		diff = diff.astype(int)

	# calculate the error		# calculate the error
	error = np.ravel(image_array[1:-1,1:-1])-predict		error = np.ravel(image_array[1:-1,1:-1])-predict

	return image_array, predict, diff, error, A		return image_array, predict, diff, error, A
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	"""		"""
	this huffman encoding code is found online		this huffman encoding code is found online
	https://favtutor.com/blogs/huffman-coding		https://favtutor.com/blogs/huffman-coding
	"""		"""

	class NodeTree(object):		class NodeTree(object):
	def __init__(self, left=None, right=None):		def __init__(self, left=None, right=None):
	self.left = left		self.left = left
	self.right = right		self.right = right

	def children(self):		def children(self):
	return self.left, self.right		return self.left, self.right

	def __str__(self):		def __str__(self):
	return self.left, self.right		return self.left, self.right


	def huffman_code_tree(node, binString=''):		def huffman_code_tree(node, binString=''):
	'''		'''
	Function to find Huffman Code		Function to find Huffman Code
	'''		'''
	if type(node) is str:		if type(node) is str:
	return {node: binString}		return {node: binString}
	(l, r) = node.children()		(l, r) = node.children()
	d = dict()		d = dict()
	d.update(huffman_code_tree(l, binString + '0'))		d.update(huffman_code_tree(l, binString + '0'))
	d.update(huffman_code_tree(r, binString + '1'))		d.update(huffman_code_tree(r, binString + '1'))
	return d		return d


	def make_tree(nodes):		def make_tree(nodes):
	'''		'''
	Function to make tree		Function to make tree
	:param nodes: Nodes		:param nodes: Nodes
	:return: Root of the tree		:return: Root of the tree
	'''		'''
	while len(nodes) > 1:		while len(nodes) > 1:
	(key1, c1) = nodes[-1]		(key1, c1) = nodes[-1]
	(key2, c2) = nodes[-2]		(key2, c2) = nodes[-2]
	nodes = nodes[:-2]		nodes = nodes[:-2]
	node = NodeTree(key1, key2)		node = NodeTree(key1, key2)
	nodes.append((node, c1 + c2))		nodes.append((node, c1 + c2))
	#reverse True, decending order		#reverse True, decending order

	#There is a huge memory leak here, no idea how or why		#There is a huge memory leak here, no idea how or why
	nodes = sorted(nodes, key=lambda x: x[1], reverse=True)		nodes = sorted(nodes, key=lambda x: x[1], reverse=True)
	return nodes[0][0]		return nodes[0][0]
	def decode_string(huffman_string, the_values, the_keys):		def decode_string(huffman_string, the_keys, the_values):
	for i in range(len(huffman_string)):		for i in range(len(huffman_string)):
	try:		try:
	return (int(the_keys[the_values.index(huffman_string[:i+1])]),huffman_string[i+1:])		return (int(the_keys[the_values.index(huffman_string[:i+1])]),huffman_string[i+1:])
	except:		except:
	pass		pass

	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def huffman(tiff_image_path, num_bins=4, difference = True):		def huffman(tiff_image_path, num_bins=4, difference = True):
	"""		"""
	This function is used to encode the error based on the difference		This function is used to encode the error based on the difference
	and split the difference into different bins		and split the difference into different bins

	Input:		Input:
	tiff_image_path (string): path to the tiff file		tiff_image_path (string): path to the tiff file
	num_bins (int): number of bins		num_bins (int): number of bins

	Return:		Return:
	huffman_encoding_list list (num_bins + 1): a list of dictionary		huffman_encoding_list list (num_bins + 1): a list of dictionary
	image_array ndarray (512, 640): original image		image_array ndarray (512, 640): original image
	new_error ndarray (512, 640): error that includes the boundary		new_error ndarray (512, 640): error that includes the boundary
	diff ndarray (510, 638): difference of min and max of the 4 neighbors		diff ndarray (510, 638): difference of min and max of the 4 neighbors
	boundary ndarray (2300,): the boundary values after subtracting the very first pixel value		boundary ndarray (2300,): the boundary values after subtracting the very first pixel value
	predict ndarray (325380,): the list of predicted values		predict ndarray (325380,): the list of predicted values
	bins list (num_bins - 1,): a list of threshold to cut the bins		bins list (num_bins - 1,): a list of threshold to cut the bins
	A ndarray (3 X 3): system of equation		A ndarray (3 X 3): system of equation

	"""		"""
	# get the image_array, etc		# get the image_array, etc
	image_array, predict, diff, error, A = predict_pix(tiff_image_path, difference)		image_array, predict, diff, error, A = predict_pix(tiff_image_path, difference)

	# calculate the number of points that will go in each bin		# calculate the number of points that will go in each bin
	data_points_per_bin = diff.size // num_bins		data_points_per_bin = diff.size // num_bins

	# sort the difference and create the bins		# sort the difference and create the bins
	sorted_diff = np.sort(diff.copy())		sorted_diff = np.sort(diff.copy())
	bins = [sorted_diff[i*data_points_per_bin] for i in range(1,num_bins)]		bins = [sorted_diff[i*data_points_per_bin] for i in range(1,num_bins)]

	# get the boundary		# get the boundary
	boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))		boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))

	# take the difference of the boundary with the very first pixel		# take the difference of the boundary with the very first pixel
	boundary = boundary - image_array[0,0]		boundary = boundary - image_array[0,0]

	#boundary is 1dim, so boundary[0] is just the first element		#boundary is 1dim, so boundary[0] is just the first element
	boundary[0] = image_array[0,0]		boundary[0] = image_array[0,0]

	# huffman encode the boundary		# huffman encode the boundary
	bound_vals_as_string = [str(i) for i in boundary]		bound_vals_as_string = [str(i) for i in boundary]
	freq = dict(Counter(bound_vals_as_string))		freq = dict(Counter(bound_vals_as_string))
	freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)		freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
	node = make_tree(freq)		node = make_tree(freq)
	huffman_encoding_dict = huffman_code_tree(node)		huffman_encoding_dict = huffman_code_tree(node)

	# create a list of huffman table		# create a list of huffman table
	huffman_encoding_list = [huffman_encoding_dict]		huffman_encoding_list = [huffman_encoding_dict]
			print(len(huffman_encoding_list))
	n = len(bins)		n = len(bins)

	# loop through different bins		# loop through different bins
	for i in range (0,n):		for i in range (0,n):
	# the first bin		# the first bin
	if i == 0 :		if i == 0 :
	# get the point within the bin and huffman huffman_encoding_dict		# get the point within the bin and huffman huffman_encoding_dict
	mask = diff <= bins[i]		mask = diff <= bins[i]
	line_as_string = [str(i) for i in error[mask].astype(int)]		line_as_string = [str(i) for i in error[mask].astype(int)]
	freq = dict(Counter(line_as_string))		freq = dict(Counter(line_as_string))
	freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)		freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
	node = make_tree(freq)		node = make_tree(freq)
	huffman_encoding_dict = huffman_code_tree(node)		huffman_encoding_dict = huffman_code_tree(node)
	huffman_encoding_list.append(huffman_encoding_dict)		huffman_encoding_list.append(huffman_encoding_dict)

	# the middle bins		# the middle bins
	else:		else:
	# get the point within the bin and huffman huffman_encoding_dict		# get the point within the bin and huffman huffman_encoding_dict
	mask = diff > bins[i-1]		mask = diff > bins[i-1]
	new_error = error[mask]		new_error = error[mask]
	mask2 = diff[mask] <= bins[i]		mask2 = diff[mask] <= bins[i]
	line_as_string = [str(i) for i in new_error[mask2].astype(int)]		line_as_string = [str(i) for i in new_error[mask2].astype(int)]
	freq = dict(Counter(line_as_string))		freq = dict(Counter(line_as_string))
	freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)		freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
	node = make_tree(freq)		node = make_tree(freq)
	huffman_encoding_dict = huffman_code_tree(node)		huffman_encoding_dict = huffman_code_tree(node)
	huffman_encoding_list.append(huffman_encoding_dict)		huffman_encoding_list.append(huffman_encoding_dict)

	# the last bin		# the last bin
	# get the point within the bin and huffman huffman_encoding_dict		# get the point within the bin and huffman huffman_encoding_dict
	mask = diff > bins[-1]		mask = diff > bins[-1]
	line_as_string = [str(i) for i in error[mask].astype(int)]		line_as_string = [str(i) for i in error[mask].astype(int)]
	freq = dict(Counter(line_as_string))		freq = dict(Counter(line_as_string))
	freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)		freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
	node = make_tree(freq)		node = make_tree(freq)
	huffman_encoding_dict = huffman_code_tree(node)		huffman_encoding_dict = huffman_code_tree(node)
	huffman_encoding_list.append(huffman_encoding_dict)		huffman_encoding_list.append(huffman_encoding_dict)

	# create a error matrix that includes the boundary (used in encoding matrix)		# create a error matrix that includes the boundary (used in encoding matrix)
	new_error = np.copy(image_array)		new_error = np.copy(image_array)
	new_error[1:-1,1:-1] = np.reshape(error,(510, 638))		new_error[1:-1,1:-1] = np.reshape(error,(510, 638))
	keep = new_error[0,0]		keep = new_error[0,0]
	new_error[0,:] = new_error[0,:] - keep		new_error[0,:] = new_error[0,:] - keep
	new_error[-1,:] = new_error[-1,:] - keep		new_error[-1,:] = new_error[-1,:] - keep
	new_error[1:-1,0] = new_error[1:-1,0] - keep		new_error[1:-1,0] = new_error[1:-1,0] - keep
	new_error[1:-1,-1] = new_error[1:-1,-1] - keep		new_error[1:-1,-1] = new_error[1:-1,-1] - keep
	new_error[0,0] = keep		new_error[0,0] = keep
	# huffman_encoding_list = list(set(huffman_encoding_list))		# huffman_encoding_list = list(set(huffman_encoding_list))
	diff = np.reshape(diff,(510,638))		diff = np.reshape(diff,(510,638))
	# return the huffman dictionary		# return the huffman dictionary
			print(len(huffman_encoding_list))
	return huffman_encoding_list, image_array, new_error, diff, boundary, predict, bins, A		return huffman_encoding_list, image_array, new_error, diff, boundary, predict, bins, A

	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def encoder(error, list_dic, diff, bound, bins):		def encoder(error, list_dic, diff, bound, bins):
	"""		"""
	This function encode the matrix with huffman coding tables		This function encode the matrix with huffman coding tables

	Input:		Input:
	error (512, 640): a matrix with all the errors		error (512, 640): a matrix with all the errors
	list_dic (num_dic + 1,): a list of huffman coding table		list_dic (num_dic + 1,): a list of huffman coding table
	bound (2300,): the boundary values after subtracting the very first pixel value		bound (2300,): the boundary values after subtracting the very first pixel value
	bins (num_bins - 1,): a list of threshold to cut the bins		bins (num_bins - 1,): a list of threshold to cut the bins

	Return:		Return:
	encoded (512, 640): encoded matrix		encoded (512, 640): encoded matrix
	"""		"""
	returnableencode = ""		returnable_encode = ""
	# copy the error matrix (including the boundary)		# copy the error matrix (including the boundary)
	encoded = np.copy(error).astype(int).astype(str).astype(object)		encoded = np.copy(error).astype(int).astype(str).astype(object)
	#diff = np.reshape(diff,(510,638))		#diff = np.reshape(diff,(510,638))
	# loop through all the pixel to encode		# loop through all the pixel to encode
	for i in range(encoded.shape[0]):		for i in range(encoded.shape[0]):
	for j in range(encoded.shape[1]):		for j in range(encoded.shape[1]):
	if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:		if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:
	returnableencode += list_dic[0][encoded[i][j]]		returnable_encode += list_dic[0][encoded[i][j]]
	elif diff[i-1][j-1] <= bins[0]:		elif diff[i-1][j-1] <= bins[0]:
	returnableencode += list_dic[1][encoded[i][j]]		returnable_encode += list_dic[1][encoded[i][j]]
	elif diff[i-1][j-1] <= bins[1] and diff[i-1][j-1] > bins[0]:		elif diff[i-1][j-1] <= bins[1] and diff[i-1][j-1] > bins[0]:
	returnableencode +=list_dic[2][encoded[i][j]]		returnable_encode +=list_dic[2][encoded[i][j]]
	elif diff[i-1][j-1] <= bins[2] and diff[i-1][j-1] > bins[1]:		elif diff[i-1][j-1] <= bins[2] and diff[i-1][j-1] > bins[1]:
	returnableencode +=list_dic[3][encoded[i][j]]		returnable_encode +=list_dic[3][encoded[i][j]]
	else:		else:
	returnableencode += list_dic[4][encoded[i][j]]		returnable_encode += list_dic[4][encoded[i][j]]

	return returnableencode		return returnable_encode
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def decoder(A, encoded_string, list_dic, bins, use_diff):		def decoder(A, encoded_string, list_dic, bins, use_diff):
	"""		"""
	This function decodes the encoded_matrix.		This function decodes the encoded_matrix.
	Input:		Input:
	A (3 X 3): system of equation		A (3 X 3): system of equation
	list_dic (num_dic + 1,): a list of huffman coding table		list_dic (num_dic + 1,): a list of huffman coding table
	encoded_matrix (512, 640): encoded matrix		encoded_matrix (512, 640): encoded matrix
	bins (num_bins - 1,): a list of threshold to cut the bins		bins (num_bins - 1,): a list of threshold to cut the bins

	Return:		Return:
	decode_matrix (512, 640): decoded matrix		decode_matrix (512, 640): decoded matrix
	"""		"""
	# change the dictionary back to list		# change the dictionary back to list
	# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins		# !!!!!WARNING!!!! has to change this part, everytime you change the number of bins
	the_keys0 = list(list_dic[0].keys())		the_keys0 = list(list_dic[0].keys())
	the_values0 = list(list_dic[0].values())		the_values0 = list(list_dic[0].values())

	the_keys1 = list(list_dic[1].keys())		the_keys1 = list(list_dic[1].keys())
	the_values1 = list(list_dic[1].values())		the_values1 = list(list_dic[1].values())

	the_keys2 = list(list_dic[2].keys())		the_keys2 = list(list_dic[2].keys())
	the_values2 = list(list_dic[2].values())		the_values2 = list(list_dic[2].values())

	the_keys3 = list(list_dic[3].keys())		the_keys3 = list(list_dic[3].keys())
	the_values3 = list(list_dic[3].values())		the_values3 = list(list_dic[3].values())

	the_keys4 = list(list_dic[4].keys())		the_keys4 = list(list_dic[4].keys())
	the_values4 = list(list_dic[4].values())		the_values4 = list(list_dic[4].values())

	#Matrix system of points that will be used to solve the least squares fitting hyperplane		#Matrix system of points that will be used to solve the least squares fitting hyperplane
	points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])		points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])

	decode_matrix = np.zeros((512,640))		decode_matrix = np.zeros((512,640))
	# loop through all the element in the matrix		# loop through all the element in the matrix
	for i in range(decode_matrix.shape[0]):		for i in range(decode_matrix.shape[0]):
	for j in range(decode_matrix.shape[1]):		for j in range(decode_matrix.shape[1]):
	# if it's the very first pixel on the image		# if it's the very first pixel on the image
	if i == 0 and j == 0:		if i == 0 and j == 0:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)
	decode_matrix[i][j] = colorvalue		decode_matrix[i][j] = colorvalue

	# if it's on the boundary (any of the 4 edges)		# if it's on the boundary (any of the 4 edges)
	elif i == 0 or i == decode_matrix.shape[0]-1 or j == 0 or j == decode_matrix.shape[1]-1:		elif i == 0 or i == decode_matrix.shape[0]-1 or j == 0 or j == decode_matrix.shape[1]-1:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)
	decode_matrix[i][j] = colorvalue + decode_matrix[0][0]		decode_matrix[i][j] = colorvalue + decode_matrix[0][0]
	# if not the boundary		# if not the boundary
	else:		else:
	# predict the image with the known pixel value		# predict the image with the known pixel value
	z0 = decode_matrix[i-1][j-1]		z0 = decode_matrix[i-1][j-1]
	z1 = decode_matrix[i-1][j]		z1 = decode_matrix[i-1][j]
	z2 = decode_matrix[i-1][j+1]		z2 = decode_matrix[i-1][j+1]
	z3 = decode_matrix[i][j-1]		z3 = decode_matrix[i][j-1]
	y0 = int(-z0+z2-z3)		y0 = int(-z0+z2-z3)
	y1 = int(z0+z1+z2)		y1 = int(z0+z1+z2)
	y2 = int(-z0-z1-z2-z3)		y2 = int(-z0-z1-z2-z3)
	y = np.vstack((y0,y1,y2))		y = np.vstack((y0,y1,y2))
	if use_diff:		if use_diff:
	difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)		difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)
	else:		else:

	f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None)		f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None)
	difference = difference.astype(int)		difference = difference.astype(int)

	predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))		predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))

	# add on the difference by searching the dictionary		# add on the difference by searching the dictionary
	# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins		# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins
	if difference <= bins[0]:		if difference <= bins[0]:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys1, the_values=the_values1)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys1, the_values=the_values1)
	decode_matrix[i][j] = colorvalue + int(predict)		decode_matrix[i][j] = colorvalue + int(predict)
	elif difference <= bins[1] and difference > bins[0]:		elif difference <= bins[1] and difference > bins[0]:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys2, the_values=the_values2)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys2, the_values=the_values2)
	decode_matrix[i][j] = colorvalue + int(predict)		decode_matrix[i][j] = colorvalue + int(predict)
	elif difference <= bins[2] and difference > bins[1]:		elif difference <= bins[2] and difference > bins[1]:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys3, the_values=the_values3)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys3, the_values=the_values3)
	decode_matrix[i][j] = colorvalue + int(predict)		decode_matrix[i][j] = colorvalue + int(predict)
	else:		else:
	colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys4, the_values=the_values4)		colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys4, the_values=the_values4)
	decode_matrix[i][j] = colorvalue + int(predict)		decode_matrix[i][j] = colorvalue + int(predict)


	return decode_matrix.astype(int)		return decode_matrix.astype(int)
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def compress_rate(image_array, new_error, diff, bound, huffman_encoding_list, bins):		def compress_rate(image_array, new_error, diff, bound, huffman_encoding_list, bins):
	'''		'''
	This function is used to calculate the compression rate.		This function is used to calculate the compression rate.
	Input:		Input:
	image_array (512, 640): original_core image		image_array (512, 640): original_core image
	new_error (512, 640): error that includes the boundary		new_error (512, 640): error that includes the boundary
	diff (510, 638): difference of min and max of the 4 neighbors		diff (510, 638): difference of min and max of the 4 neighbors
	bound (2300,): the boundary values after subtracting the very first pixel value		bound (2300,): the boundary values after subtracting the very first pixel value
	huffman_encoding_list (num_dic + 1,): a list of huffman coding table		huffman_encoding_list (num_dic + 1,): a list of huffman coding table
	bins (num_bins - 1,): a list of threshold to cut the bins		bins (num_bins - 1,): a list of threshold to cut the bins

	Return:		Return:
	compression rate		compression rate
	'''		'''
	# the bits for the original image		# the bits for the original image
	o_len = 0		o_len = 0
	# the bits for the compressed image		# the bits for the compressed image
	c_len = 0		c_len = 0
	# initializing the varible		# initializing the varible

	#this was unused		#this was unused
	# im = np.reshape(image,(512, 640))		# im = np.reshape(image,(512, 640))

	real_boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))		real_boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))
	#Bryce's notes: Why are they all reshaped?		#Bryce's notes: Why are they all reshaped?
	original_core = image_array[1:-1,1:-1].reshape(-1)		original_core = image_array[1:-1,1:-1].reshape(-1)
	diff = diff.reshape(-1)		diff = diff.reshape(-1)
	error = new_error[1:-1,1:-1].reshape(-1)		error = new_error[1:-1,1:-1].reshape(-1)

	# calculate the bit for boundary		# calculate the bit for boundary
	for i in range(0,len(bound)):		for i in range(0,len(bound)):
	o_len += len(bin(real_boundary[i])[2:])		o_len += len(bin(real_boundary[i])[2:])
	c_len += len(huffman_encoding_list[0][str(bound[i])])		c_len += len(huffman_encoding_list[0][str(bound[i])])

	# calculate the bit for the pixels inside the boundary		# calculate the bit for the pixels inside the boundary
	for i in range(0,len(original_core)):		for i in range(0,len(original_core)):

	# for the original image		# for the original image
	o_len += len(bin(original_core[i])[2:])		o_len += len(bin(original_core[i])[2:])

	# check the difference and find the coresponding huffman table		# check the difference and find the coresponding huffman table
	# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins		# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins
	if diff[i] <= bins[0]:		if diff[i] <= bins[0]:
	c_len += len(huffman_encoding_list[1][str(int(error[i]))])		c_len += len(huffman_encoding_list[1][str(int(error[i]))])

	elif diff[i] <= bins[1] and diff[i] > bins[0]:		elif diff[i] <= bins[1] and diff[i] > bins[0]:
	c_len += len(huffman_encoding_list[2][str(int(error[i]))])		c_len += len(huffman_encoding_list[2][str(int(error[i]))])

	elif diff[i] <= bins[2] and diff[i] > bins[1]:		elif diff[i] <= bins[2] and diff[i] > bins[1]:
	c_len += len(huffman_encoding_list[3][str(int(error[i]))])		c_len += len(huffman_encoding_list[3][str(int(error[i]))])

	else:		else:
	c_len += len(huffman_encoding_list[4][str(int(error[i]))])		c_len += len(huffman_encoding_list[4][str(int(error[i]))])

	return c_len/o_len		return c_len/o_len
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	scenes = file_extractor()		scenes = file_extractor()
	images = image_extractor(scenes)		images = image_extractor(scenes)
	list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)		list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)
	encoded_string = encoder(new_error, list_dic, diff, bound, bins)		encoded_string = encoder(new_error, list_dic, diff, bound, bins)
	reconstruct_image = decoder(A, encoded_string, list_dic, bins, False)		reconstruct_image = decoder(A, encoded_string, list_dic, bins, False)
	print(np.allclose(image, reconstruct_image))		print(np.allclose(image, reconstruct_image))
	print(len(list_dic))		print(len(list_dic))
	```		```

	%% Output		%% Output

	True		1
	5		5

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	compress_rate(image, new_error, diff, bound, list_dic, bins)		compress_rate(image, new_error, diff, bound, list_dic, bins)
	```		```

	%% Output		%% Output

	0.4232928466796875		0.4232928466796875

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	print(sys.getsizeof(encoded_string))		print(sys.getsizeof(encoded_string))
	with open("MatrixNowString.txt", 'wb') as f:		with open("MatrixNowString.txt", 'wb') as f:
	f.write(bytearray(encoded_string, encoding = 'utf8'))		f.write(bytearray(encoded_string, encoding = 'utf8'))
	```		```

	%% Output		%% Output

	2080618		2080618

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	print(os.path.getsize('images/1626032610_393963/1626032610_393963_0.tiff'))		print(os.path.getsize('images/1626032610_393963/1626032610_393963_0.tiff'))
	```		```

	%% Output		%% Output

	657197		657197

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	print(os.path.getsize('MatrixNowString.txt'))		print(os.path.getsize('MatrixNowString.txt'))
	```		```

	%% Output		%% Output

	398145		2080569

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	def bitstring_to_bytes(s):		def bitstring_to_bytes(s):
	v = int(s, 2)		v = int(s, 2)
	b = bytearray()		b = bytearray()
	while v:		while v:
	b.append(v & 0xff)		b.append(v & 0xff)
	v >>= 8		v >>= 8
	return bytes(b[::-1])		return bytes(b[::-1])

	s = "0110100001101001"		s = "0110100001101001"
	inletters = bitstring_to_bytes(encoded_string)		inletters = bitstring_to_bytes(encoded_string)

	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	```		```

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	print(sys.getsizeof(encoded_string))		print(sys.getsizeof(encoded_string))
	with open("MatrixNowString.txt", 'w') as f:		with open("MatrixNowString.txt", 'w') as f:
	f.write(inletters.decode("ISO-8859-1"))		f.write(inletters.decode("ISO-8859-1"))
	```		```

	%% Output		%% Output

	2080618		2080618

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	(os.path.getsize('MatrixNowString.txt'))/os.path.getsize('images/1626032610_393963/1626032610_393963_0.tiff')		(os.path.getsize('MatrixNowString.txt'))/os.path.getsize('images/1626032610_393963/1626032610_393963_0.tiff')
	```		```

	%% Output		%% Output

	0.6058229115470704		0.6058229115470704

	%% Cell type:code id: tags:		%% Cell type:code id: tags:

	``` python		``` python
	```		```

			%% Cell type:code id: tags:

			``` python
			```

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